Method and apparatus to improve an mri image

ABSTRACT

An MRI imaging system includes at least one processor and a plurality of coils to acquire a plurality of k-space samples of a target to image. The system includes a machine-readable media comprising instructions which, when executed by the processor, result in determining a plurality of different regularization matrices for a plurality of different regions of an image of the target. The regularization matrices are applied in the determination of a plurality of unmixing matrices for the regions. The unmixing matrices are applied to produce the image without ghost artifacts, from a plurality of MRI images produced from the plurality of k-space samples and each comprising ghost artifacts.

RELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional PatentApplication No. 60/348,005 filed Oct. 19, 2001.

TECHNICAL FIELD

[0002] The disclosure relates generally to Magnetic Resonance Imaging(MRI), and more particularly to artifact cancellation in MR generatedimages.

BACKGROUND

[0003] Magnetic Resonance Imaging (MRI) is an imaging technique based inpart on the absorption and emission of energy in the radio frequencyrange. To obtain the necessary magnetic resonance (MR) images, a patient(or other target) is placed in a magnetic resonance scanner. The scannerprovides a magnetic field that causes magnetic moments in the patient ortarget atoms to align with the magnetic field. The scanner also includescoils that apply a transverse magnetic field. RF pulses are emitted bythe coils, causing the target atoms to absorb energy. In response to theRF pulses, photons are emitted by the target atoms and detected assignals in receiver coils.

[0004] The signals detected in the receiver coils may be processed toconstruct an image of the target. The signals may be made proportionalto the spatial frequency content (k-space) of the image through theproper application of gradients to the magnetic field. The k-space maycomprise sets of samples, called lines, each line corresponding to asingle phase encoding of the sampling process. It is well known that thenumber and spacing of lines in k-space determines both the field of view(FOV) and the spatial resolution of the reconstructed image.

[0005] Data processing may be performed on the k-space samples toproduce a final image of the object in “image space”, e.g. a spatialarrangement of pixels. The data processing is typically performed usinga computer, which is any device comprising a processor and memory,wherein the processor executes instructions and acts upon data providedfrom the memory.

[0006] Rapid imaging is desirable in order to reduce the time requiredto perform volume imaging consisting of a large number of slices, toreduce the breath-hold time, or for dynamic imaging applications such asfunctional imaging of the heart or brain. Rapid imaging also providesincreased motion tolerance. A number of accelerated imaging methods havebeen developed. In several of these methods, undesirable “ghost”artifacts arise when the k-space samples are processed into the imagedomain. In one such method, known as echo-planar imaging (EPI),distortions in k-space may lead to image domain ghosts. In another suchmethod, known as SENSE, intentional k-space undersampling (samplingfewer lines than the number required to image a chosen field-of-view)accelerates the data acquisition but results in image domain ghosts dueto aliasing. For more details on SENSE see Pruessmann et al., SENSE:Sensitivity Encoding for Fast MRI, Magnetic Resonance in Medicine, 1999Nov; 42(5): 952-962.) With the SENSE approach, ghost artifacts whicharise from aliasing may be suppressed in the image by way of a techniqueknown as “phased array combining”. Phased array combining may be appliedto suppress ghost artifacts arising from a variety of mechanisms, notjust aliasing. U.S. patent application Ser. No. 09/825,617, entitledGhost Artifact Cancellation Using Phased Array Processing, and filed onApr. 3, 2001, by Kellman et al. (henceforth “Kellman 1”), teaches onesuch phased array combining approach.

[0007] Phased array combining approaches for ghost cancellation(including SENSE) involve combining multiple intermediate images, eachcomprising ghost artifacts, to produce a final image in which ghostartifacts are suppressed. Often, the intermediate images are combined ina manner which is numerically ill-conditioned, so that noise in theintermediate images as well as errors in the combining weights (broughton, for instance, by noise in the operation and characterization of thesignal reception process) may amplify noise in the final image. Onetechnique to mitigate this problem is called regularization or matrixconditioning. Regularization involves a tradeoff between a level ofghost artifact suppression and noise amplification. Current approachesapply a fixed amount of regularization to all pixels of an image. Suchapproaches do not take into account that particular regions (sets of oneor more pixels) of the final image may benefit from substantially lessghost suppression than others, and therefore can benefit from greaternoise reduction by trading off more ghost suppression than in otherregions of the image.

SUMMARY OF THE DISCLOSURE

[0008] In one aspect, a MRI imaging system includes at least oneprocessor and coils to acquire k-space samples of a target to image. Thesystem includes a machine-readable media comprising instructions which,when executed by the processor, result in determining differentregularization matrices for different regions of an image of the target.The regularization matrices are applied in the determination of unmixingmatrices for the different pixel positions. The unmixing matrices areapplied to produce the image without ghost artifacts from intermediateMRI images produced from the plurality of k-space samples, theintermediate images each having ghost artifacts.

[0009] In another aspect, a MRI imaging system includes coils to acquirereduced k-space samples for intermediate images. An apparatus comprisingat least one processor executes instructions to combine the intermediateimages to produce a full field of view image, by applying unmixingmatrices. Each unmixing matrix is regularized according to a targetlevel of alias suppression for a region of the full field of view image.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010]FIG. 1 is a high-level block diagram of an MRI method embodiment.

[0011]FIG. 2 is a more detailed block diagram of an MRI methodembodiment.

[0012]FIG. 3 is a block diagram showing an embodiment of data processingto reduce ghost artifacts in the final image.

[0013]FIG. 4 is a block diagram showing an embodiment of an adaptive,spatially-variant regularization method.

[0014]FIG. 5 is a block diagram of an apparatus embodiment.

DETAILED DESCRIPTION

[0015] In the following description and figures, like numbers refer tolike elements. References to “one embodiment” and “an embodiment” do notnecessarily refer to the same embodiment, although they may.Furthermore, the singular terms “a,” “an,” and “the” include pluralreferents unless the context clearly indicates otherwise.

[0016] Throughout this description, embodiments may be described whichapply matrix regularization on a pixel-by-pixel basis. Other embodimentsmay operate in substantially similar manners but may regularizeaccording to regions of an image larger than a single pixel (forexample, upon groups of neighboring pixels). In the figures, images maybe illustrated as pixel maps. These pixel maps are provided forillustration purposes only and may represent, in some instances, thecomplex values from which the pixel intensity magnitudes are generated.

[0017] Overview

[0018]FIG. 1 is a high-level block diagram of an MRI method embodiment100. A set of k-space samples is acquired from N_(c) receiver coils,where N_(c) is an integer number. For example, N_(c)=4 when four coilsare employed. Data processing is performed at 102 to produce a finalimage 104. In general, the data processing involves (1) producing aplurality of intermediate images from the reduced k-space samples, and(2) combining the intermediate images into a final image. Theintermediate images may contain ghost artifacts arising from the k-spaceacquisition, for example arising from EPI distortions or undersampling.The intermediate images may be combined to produce the final image whilesuppressing ghost artifacts.

[0019] For simplicity, the following discussion applies to anapplication comprising a single ghost artifact in each intermediateimage. The discussion is generally applicable to situations involving agreater number of ghost artifacts as well.

[0020] Acquiring the Intermediate Images

[0021]FIG. 2 is a more detailed block diagram of a MRI method embodiment200. MR coils (in this example, coil1, coil2, coil3, and coil4) may bepositioned in differing aspects relative to an object to sample. K-spacesamples may be acquired for each coil. At 201, 202, 203, and 204, an FFToperation is applied to each set of acquired k-space samples, resultingin intermediate images 205, 206, 207, and 208, respectively. In thisexample, each of the intermediate images 205-208 is comprised of thedesired image plus a single ghost artifact. The ghost artifact in thisexample is a shifted version of the desired final image, with a verticalshift equal to FOV/2 pixels. This situation may arise in SENSEapplications where image acquisition is accelerated by a factor R=2,where each set of k-space samples comprises FOV/2 lines, as well as inother applications such as EPI. The intermediate images 205-208 in thisexample comprise pixels which are a superposition of a desired pixelvalue and a ghost pixel value. The number of superpositions at a pixellocation is equal to R, the acceleration factor. Thus, for R=2, a pixelposition (x,y) in each intermediate image may comprise pixel valueswhich are a superposition (sum) of (1) the pixel value at position (x,y)in the final image, and (2) the pixel value from a position (x,y+FOV/2).(More specifically, position (x, (y+FOV/2) mod FOV) where FOV is thepixel height of the image. Henceforth, the position (y+FOV/2) mod FOV)will be referred to simply as y_(alias).) This ghosting effect is alsoreferred to as “fold over” and “mixing”.

[0022] Data processing 102 may be applied to combine the intermediateimages 205-208 to produce the final image 104. When combining, properweighting of the pixel values of the intermediate images 205-208 mayproduce pixels in the final image 104 with suppressed ghost artifacts.

[0023] Combining the Intermediate Images

[0024]FIG. 3 is a block diagram showing one embodiment 300 of dataprocessing to suppress ghost artifacts in the final image. Pixel valuesp_(i)(x,y) from corresponding positions (x,y) of the four intermediateimages 205-208 may be processed to produce a final image 104 withsuppressed ghost artifacts, where i has the range 1 to 4 (in thisexample with 4 coils). Through application of an unmixing matrix at 306,the pixels p_(i)(x,y) of the intermediate images 205-208 may be weightedand added together to produce a pixel q(x,y) of the final image 104.Noise may be introduced into the final image due to both (1) noise inthe received k-space 30 samples, and (2) inaccuracies in the weightsapplied to the pixels of the intermediate images. The inaccuracies inthe weights, in turn, may result from inaccuracies in the estimated MRcoil sensitivities, among other things. The level of noise introducedinto the final image is dependent upon the weights. The noise may bereduced at the expense of reduced artifact suppression.

[0025] For N_(c)=4, one pixel from each position (x,y) of theintermediate images 205-208 are arranged into a 4×1 (N_(c)×1) vector P.Application of the unmixing matrix may transform P into matrix Qcomprising pixel values of the final image 104. In other words, theintermediate images 205-208, when taken together, comprise enoughinformation to separately resolve all pixel values in the final image104.

[0026] The transformation of P to Q, e.g. the separation of superimposedpixels of the intermediate images 205-208 into non-superimposed pixelsof the final image 104, may be accomplished by application of theunmixing matrix U.

Q=U·P

[0027] In the SENSE accelerated imaging application, where intermediateimages are comprised of R superimposed aliased pixels, the unmixingmatrix U is typically formulated as a 2×N_(c) (R×N_(c)) with pixelslocations (x,y) evaluated over FOV/2, which produces a 2×1 (R×1) vectorQ, with elements corresponding to (x,y) and (x,y_(alias)). The unmixingmatrix may equivalently be formulated with U defined as a 1×Nc vectorand pixels locations (x,y) taken from the full FOV.

[0028] A result of the matrix multiplication of U and P is that eachelement of Q represents a weighted sum of N_(c) pixels, one from eachcorresponding position (x,y) of the intermediate images 205-208. Theelements of U are determined such that this weighted sum suppressesghosting effects which may be present in the pixels of the intermediateimages 205-208. In other words, the weighted sum produced by U for eachpixel position (x,y) of the intermediate images 205-208 separates thepixel values at that position. The degree of such separation may vary,for reasons and in manners described below.

[0029] The elements of U may be determined from transformationsinvolving an N_(c)×R matrix S. Matrix S is referred to as the“sensitivity matrix”. Each row i of S corresponds to the “sensitivity”of coil i at a plurality of pixel positions. For R=2, each column j of Scomprises (1) a coil sensitivity value for the pixel at position (x,y)of the final image 104, and (2) a coil sensitivity value for the pixelat position (x,y_(alias)) of the final image 104. The pixels atpositions (x,y) and (x, y_(alias)) of the final image are the pixelswhich superimpose at position (x,y) in the intermediate images 205-208.

[0030] Assuming that the elements of S perfectly represent of the actualsensitivities of the coils, then one manner of determining the unmixingmatrix U from S involves applying the transformation

U ₀=(S ^(H)ψ⁻¹ S)⁻¹ S ^(H)ψ⁻¹

[0031] where S^(H) represents the conjugate transpose (Hermitianoperation) of matrix S, the negative exponent (−1) indicates a matrixinversion operation, and ψ represents the well-known noise covariancematrix for the receiver coils. Here, U₀ represents an intermediatedetermination of U which may comprise an undesirable gain aspect.Manners of compensating for this gain aspect to produce the final matrixU are more fully described below.

[0032] Typically, the elements of S are not perfect representations ofthe actual sensitivities of the coils. It may not be possible toexperimentally determine the coil sensitivities with complete accuracyfor a particular imaging operation. Furthermore, the sensitivity valuesmay vary according to interactive effects between coils, motion of thetarget object, and other variables. Thus, the matrix S may compriseerrors which deviate from the actual sensitivity values of the coils.Furthermore, the k-space samples may comprise noise which may add to thepixel values of the intermediate images 205-208. Application of theunmixing matrix U to the pixels of the intermediate images 205-208 mayamplify this noise, and errors resulting from the errors in S, toundesirable levels in the final image 104.

[0033] It may be possible to reduce some of the effects of noise, anderrors in S, by applying regularization to the determination of U, inmanners which are further described below. Furthermore, an adaptiveapproach to determination of the sensitivity values may lead to reducederrors in S and thus improve ghost artifact suppression in the finalimage 104.

[0034] Determination of Coil Sensitivity Values

[0035] In one embodiment, coil sensitivity values may be determined byacquiring full FOV reference images for each coil. These referenceimages may be free of substantial ghost artifacts. These referenceimages may be acquired either before or after the desired imagingoperation (for example, accelerated imaging) by performing a ‘referencescan’.

[0036] In another embodiment, the reference images may be acquired, atleast in part, during the course of the imaging operation. One suchapproach is described in U.S. patent application Ser. No.09/735,263,entitled Accelerated Magnetic Resonance Imaging, and filed on Dec. 11,2000, by Kellman et al (henceforth “Kellman 2”). Kellman 2 teaches amanner in which full FOV k-space samples may be acquired during thecourse of an accelerated imaging operation and processed into referenceimages. The reference images may then be applied to adaptively determinethe sensitivity values of the coils at different times during the courseof the accelerated imaging operation. In other words, both acceleratedreduced k-space sampling and slower, full FOV k-space sampling takeplace over the course of the imaging operation. The images derived fromthe full FOV samples are applied to adaptively determine sensitivityvalues for the receiver coils.

[0037] In this manner, image target motion and other environmentalchanges that may effect coil sensitivities may be taken into accountduring the course of accelerated imaging. The reference images are fullFOV, and thus take longer to acquire, than do the accelerated reducedk-space images. In other words, the reference images have a lowertemporal resolution than reduced k-space images, and among otherdistortions may contain blurring effects due to rapid image targetmotion (for example, the ventricular motion of a beating heart).However, coil sensitivities adaptively estimated from such referenceimages may nonetheless prove more accurate over the course of theimaging operation than sensitivities estimated once, prior to theimaging operation.

[0038] In addition to adaptively estimating the coil sensitivities, itmay be possible to further reduce noise effects in the final image 104by compromising some ghost artifact suppression. Noise effects in thefinal image 104 may be further reduced, at the expense of ghost artifactsuppression, by “regularizing” or “better conditioning” the matrixinverse operation (S^(H)ψ⁻¹S)⁻¹ in the determination of matrix U. Onemanner of regularization involves adjustments to the elements of theterm (S^(H)ψ⁻¹S), such that inversion of the term results in less noiseamplification. Using this approach, the regularization may be performedby the addition of a matrix A, taking the form

S ^(H)ψ⁻¹ S+Λ)⁻¹ S ^(H)ψ⁻¹

[0039] Thus, the regularized determination of matrix U becomes

U ₀=(S ^(H)ψ⁻¹ S+Λ)⁻¹ S ^(H)ψ⁻¹

[0040] Again, U₀ represents a determination of U which may comprise anundesirable gain aspect and which may be compensated for in manners tobe described. Prior art regularization techniques have applied adiagonal R×R matrix A in which the diagonal elements of Λ have constantvalues near but slightly greater than the smallest eigenvalues of theterm S^(H)ψ⁻¹S. See for example SENSE Image Quality Improvement UsingMatrix Regularization, K. F. King et al., Proceedings of theInternational Society of Magnetic Resonance in Medicine 9, 1771 (2001).In the prior art, the elements of matrix A are constant for all pixelpositions, and are not adaptively determined during the course of animaging operation.

[0041] Adaptive Determination of Regularization Values

[0042]FIG. 4 is a block diagram showing an embodiment 400 of anadaptive, spatially-variant regularization method. In one embodiment, Λis a diagonal R×R matrix with element values determined according to atarget level of ghost artifact suppression to apply to one or morepixels in the final image. The target level of ghost artifactsuppression to apply, and the coil sensitivities, may be adaptivelydetermined according to reference images acquired during the course ofan imaging operation, as well as static reference images acquired beforeand/or after the imaging operation.

[0043] In one embodiment, a set of reference images r_(i) (one for eachcoil from which k-samples are acquired) is applied to determine thesensitivity matrix S at 404. The reference images r_(i) may be combinedto produce a ‘combined-magnitude’ reference image r_(cm) which isapplied to determine, at 402, a target level of ghost artifactsuppression to apply to each pixel of the final image. In oneembodiment, the value of a pixel r_(cm)(x,y) comprises the combinedmagnitude of the corresponding pixel values in r_(i,) e.g. the squareroot of the sum of the squares of the complex pixel values r_(i)(x,y).In another embodiment, for which generalized phased array ghostcancellation produces R separated ghosts (as described in Kellman1), thecombined magnitude for each individual separated ghost image may beinput to the determination of target ghost suppression, at 402. In thiscase, the target artifact suppression may be calculated as the ratio ofdesired pixel and ghost pixel using pixels in separated images. Thesensitivity matrix S may be calculated from either a single image (asshown in FIG. 4) or from multiple separated ghosts as described inKellman1. In another embodiment, the combined magnitude reference imager_(cm)(x,y) used for calculating the regularization matrices may becalculated from an initial application of unmixing using unmixingmatrices (U₀) calculated using a smaller fixed regularization or withoutany regularization.

[0044] Consider a pixel at position (x,y) of the final image. For R=2,the corresponding pixel in the intermediate images will have a valuewhich is the superposition (sum) of the pixel values in the final imageat positions (x,y) and (x,y_(alias)). Thus, in one embodiment, thetarget level of ghost artifact suppression to apply to the pixel atposition (x,y) of the final image is proportional to the ratio r_(cm)(x,y_(alias))/r_(cm)(x,y). For example, if the pixel at position (x,y) hasan intensity value of one (1), and the intensity value of the pixel atposition (x, y_(alias)) is five (5), the ratio is 5:1. A target level ofghost artifact suppression to apply to the pixel at position (x,y) maybe around five times larger than a target level to apply to a pixel at aposition where the ratio is closer to one.

[0045] The target levels of ghost artifact suppression may be chosenaccording to various criteria In one embodiment, the target level ofghost artifact suppression to apply to a pixel at a position (x,y) ischosen as a percentage of the intensity value of the pixel in thereference image. In another embodiment, a level of noise present in apixel value at position (x,y) of the reference image is determined. Atarget level of ghost artifact suppression is chosen to reduce the ghostartifact of the pixel to a level on order with the level of noise.

[0046] Coil sensitivities are estimated at 404. The coil sensitivitiesmay be estimated from the reference image in various manners, forexample in the manners detailed in Kellman 2. The estimated coilsensitivities S are provided to determine the unmixing matrix U at 408.

[0047] At 406, the regularization matrix is determined according to thetarget levels of ghost artifact suppression. In one embodiment, initialvalues are chosen for the elements of the regularization matrix Λ. At410, actual levels of ghost artifact suppression for each pixel of thefinal image are determined from the matrix U which was determinedaccording to (1) this initial Λ, and (2) the estimated S. The noisecovariance may be incorporated for optimized SNR as in previousdescribed matrix formulation for U. The noise covariance may be aseparate noise-only reference scan or estimated during imaging fromnoise-only pixels. Iterative adjustments to the elements of Λ are madeuntil the target level of ghost artifact suppression is achieved. Foreach iteration, the actual level of ghost artifact suppression ischecked with the target level of ghost artifact suppression for thepixel, and the element values of Λ are adjusted accordingly, ifnecessary, to bring the actual level of ghost artifact suppressioncloser to the target level.

[0048] An actual level of ghost artifact suppression for a pixel atposition (x,y) of the final image may be determined from the matrixproduct,

ρ=U·S

[0049] where the diagonal of ρ may be normalized to all ones (1s). ForR=2, the off-diagonal elements of ρ are then each proportional to theactual ghost artifact suppression applied to the pixels at positions(x,y) and (x, y_(alias)). For R=2, adjustments to the diagonal elementsof A may independently affect the elements of ρ. In other words,adjusting a particular diagonal element of Λ may independently affectthe actual ghost artifact suppression for a particular pixel of thefinal image. For R=2, adjusting element A_(2,2) affects the actual ghostartifact suppression represented by element ρ_(1,2), independent ofρ_(2,1). Likewise, adjusting element Λ_(1,1) affects the actual ghostartifact suppression represented by element ρ_(2,1), independent ofρ_(1,2).

[0050] In one embodiment, this process may be repeated for each pixel ofthe final image until the actual ghost artifact suppression is inaccordance with the target level. Of course, other manners ofdetermining the values of Λ which achieve the desired ghost artifactsuppression may also be employed, such as closed-end solutions, which donot involve an iterative process.

[0051] At various stages of the imaging operation, a new reference imagemay be provided to update the determination of target ghost artifactsuppression levels and coil sensitivities. See Kellman 2 for adescription of one manner in which this may be done. To compensate formotion distortions in the low temporal resolution reference images, an‘order filter’ may be applied in one embodiment. Corresponding elementsof the determined regularization matrix Λ may be compared within aneighborhood of pixels. The elements of the Λ matrix for the pixel atthe center of the neighborhood may then be set to the minimum elementvalues of the Λ matrices for all pixels in the neighborhood. Forexample, consider the following 3×3 pixel neighborhood

[0052] p₁p₂p₃

[0053] p₄p₅p₆

[0054] p₇p₈p₉

[0055] The matrix A for p₅ may be set to comprise the minimum elementvalues of Λ for the set of pixels P₁-p₉ This process may be repeated foreach pixel of the final image to reduce errors related to the lowtemporal resolution of the reference image.

[0056] Adjusting the Gain

[0057] Recall that in one embodiment, an unmixing matrix U₀ comprising again aspect is determined by

U ₀=(S ^(H)ψ⁻¹ S+Λ)⁻¹ S ^(H)ψ⁻¹

[0058] In one embodiment, a gain matrix G may be included into thedetermination of U, to compensate for the gain aspect of U₀, as follows,

U=G·U ₀ =G(S ^(H)ψ⁻¹ S+Λ)⁻¹ S ^(H)ψ⁻¹

[0059] For a diagonal matrix Λ, the term G(S^(H)ψ⁻¹S+Λ)⁻¹ approachesG(Λ)⁻¹ as the values of the diagonal elements of Λ are increased. In oneembodiment, the term G(S^(H)ψ⁻¹S+Λ)⁻¹ may be reduced to G(Λ)⁻¹ when thediagonal values of Λ are substantially larger than the maximumeigenvalues of the term S^(H)ψ⁻¹S. In this case,

U=G(Λ)⁻¹ S ^(H)ψ⁻¹ (approximately)

[0060] It is known that, in the absence of ghost artifacts, optimalsignal-to-noise ratio (SNR) may be achieved in the final image where Uis proportional to S^(H)ψ⁻¹. However, in this case no ghost artifactsuppression takes place. See for example The NMR Phased Array, Roemer etal., Magnetic Resonance in Medicine 1990; 16:192-225 (henceforthRoemer). In one embodiment, when the target ghost artifact suppressionfor a pixel is low, the term G(Λ)⁻¹ may be set to approximately theidentity matrix I, in which the value of all diagonal elements isapproximately one. Thus,

U=G(Λ)⁻¹ S ^(H)ψ⁻¹ =IS ^(H)ψ⁻¹ =S ^(H)ψ⁻¹

[0061] In other words, for pixels where ghost artifact suppression isnot substantially needed, the elements of the matrices G and Λ may bedetermined such that the SNR for the pixel in the final image is closeto the optimum levels as determined, for example, in Roemer.

[0062] For pixels where the ghost artifact suppression to apply issubstantial, G may be determined such that the diagonal elements of thematrix product G·ρ are close to one. In other words,$G \approx \begin{bmatrix}\frac{1}{\rho_{11}} & 0 \\0 & \frac{1}{\rho_{22}}\end{bmatrix}$

[0063] where ρ₁₁ and ρ₂₂ are diagonal elements of the matrix ρ₀=U₀·S. Asa consequence of compensating for the gain aspect of U₀, the pixels inthe final image may have a more desirable intensity.

[0064]FIG. 5 is a block diagram of an apparatus embodiment 500. Theapparatus 500 comprises a processing unit 502 (e.g., a processor,microprocessor, micro-controller, etc.) and machine-readable media 504.Depending on the configuration and application (mobile, desktop, server,etc.), the memory 504 may be volatile (such as RAM), non-volatile (suchas ROM, flash memory, etc.) or some combination of the two. By way ofexample, and not limitation, machine readable media 504 may comprisevolatile and/or nonvolatile media, removable and/or non-removable media,including: RAM, ROM, EEPROM, flash memory or other memory technology,CD-ROM, digital versatile disks (DVD) or other optical storage, magneticcassettes, magnetic tape, magnetic disk storage or other magneticstorage devices, or any other medium which can be used to store thedesired information to be accessed by the apparatus 500. The machinereadable media 504 may be implemented in any method or technology forstorage of information such as computer readable instructions, datastructures, program modules or other data.

[0065] The media 504 may comprise instructions and/or data which, whenexecuted by the processor 502, may result in the apparatus 500 carryingout acts in accordance with embodiments of the methods described herein.

[0066] The apparatus 500 may comprise additional storage (removable 506and/or non-removable 507) such as magnetic or optical disks or tape. Theapparatus 500 may further comprise input devices 510 such as a keyboard,pointing device, microphone, etc., and/or output devices 512 such asdisplay, speaker, and printer. The apparatus 500 may also typicallyinclude network connections 520 (such as a network adapter) for couplingto other devices, computers, networks, servers, etc. Using either wiredor wireless signaling media.

[0067] The components of the device may be embodied in a distributedcomputing system. For example, a terminal device may incorporate inputand output devices to present only the user interface, whereasprocessing component of the system are resident elsewhere. Likewise,processing functionality may be distributed across a plurality ofprocessors.

[0068] The apparatus may generate and receive machine readableinstructions, data structures, program modules or other data in amodulated data signal such as a carrier wave or other transportmechanism. These instructions and/or data may, when executed by theprocessor 502, result in acts in accordance with procedures of thepresent invention. The term “modulated data signal” means a signal thathas one or more of its characteristics set or changed in such a manneras to encode information in the signal. By way of example, and notlimitation, communication media includes wired media such as a wirednetwork or direct-wired connection, and wireless media such as acoustic,RF, infrared and other wireless media. Communications media, includingcombinations of any of the above, should be understood as within thescope of machine readable media.

[0069] Having described and illustrated the present invention withreference to one or more illustrated embodiments, it will be recognizedthat the illustrated embodiments can be modified in arrangement anddetail without departing from the principles and scope of the presentinvention. It should be understood that the programs, processes, ormethods described herein are not related or limited to any particulartype of data processing apparatus, unless indicated otherwise. Varioustypes of general purpose or specialized data processing apparatus,including desktop computers and workstations, may be used with orperform operations in accordance with the teachings described herein.Elements of the illustrated embodiments may be implemented in software,hardware, firmware, or combinations thereof

[0070] In view of the many possible embodiments to which the principlesof the present invention may be applied, it should be recognized thatthe detailed embodiments are illustrative only and should not be takenas limiting in scope. Rather, the present invention encompasses all suchembodiments as may come within the scope and spirit of the followingclaims and equivalents thereto.

We claim:
 1. A computer-implemented method, comprising: determining aplurality of different regularization matrices for a plurality ofdifferent regions of an image; applying the regularization matrices inthe determination of a plurality of unmixing matrices for the differentregions; and applying the unmixing matrices to a plurality ofundersampled MRI images with ghost artifacts to generate the imagewithout ghost artifacts.
 2. The method of claim 1 wherein determining aplurality of different regularization matrices further comprises:adaptively determining the different regularization matrices accordingto a plurality of reference images acquired over the course of animaging operation.
 3. The method of claim 2 wherein determining aplurality of different regularization matrices further comprises:determining the regularization matrices according to a plurality ofdifferent target ghost suppression levels for the different regions ofthe image.
 4. The method of claim 1 wherein the determination of aplurality of unmixing matrices for the plurality of different regionsfurther comprises: adaptively determining coil sensitivity valuesaccording to a plurality of reference images acquired over the course ofan imaging operation; and applying the adaptively determined coilsensitivity values to the determination of the unmixing matrices.
 5. Themethod of claim 3 wherein determining a plurality of differentregularization matrices further comprises: adapting the plurality ofregularization matrices according to differences between actual ghostsuppression levels for the plurality of pixel positions and theplurality of different target ghost suppression levels for the pluralityof regions.
 6. The method of claim 1 wherein determining a plurality ofdifferent regularization matrices for a plurality of different regionsof an image further comprises: determining the regularization matrix fora first region of the different regions from the minimum element valuesof the regularization matrices of surrounding regions.
 7. The method ofclaim 1 in which each region comprises a single pixel of the image. 8.The method of claim 6 in which each region comprises a single pixel ofthe image.
 9. The method of claim 3 in which the plurality of targetghost suppression levels are chosen as a percentage of an intensityvalue of the different regions.
 10. The method of claim 3 in which alevel of noise present in the different regions is determined and theplurality of target ghost suppression levels are chosen to reduce aghost artifact of the different regions to a level on order with thelevel of noise.
 11. A method comprising: acquiring a plurality ofundersampled MRI images; and combining the plurality of undersampled MRIimages to produce a full field of view image by applying a plurality ofunmixing matrices, each unmixing matrix regularized according to atarget level of alias suppression for a region of the full field of viewimage.
 12. The method of claim 11 further comprising: adjusting thetarget level of alias suppression according to reference images acquiredover the course of an imaging operation.
 13. An MRI imaging systemcomprising: at least one processor; a plurality of coils to acquire aplurality of k-space samples of a target to image; and amachine-readable media comprising instructions which, when executed bythe processor, result in determining a plurality of differentregularization matrices for a plurality of different regions of an imageof the target; applying the regularization matrices in the determinationof a plurality of unmixing matrices for the regions; and applying theunmixing matrices to produce the image without ghost artifacts from aplurality of MRI images produced from the plurality of k-space samplesand each comprising ghost artifacts.
 14. The system of claim 13 whereinthe instructions, when executed by the processor, further result in:adaptively determining the different regularization matrices accordingto a plurality of reference images acquired over the course of animaging operation of the target.
 15. The system of claim 14 wherein theinstructions, when executed by the processor, further result in:determining the regularization matrices according to a plurality ofdifferent target ghost suppression levels for the regions of the image.16. The system of claim 13 wherein the instructions, when executed bythe processor, further result in: adaptively determining sensitivityvalues for the coils according to a plurality of reference imagesacquired over the course of an imaging operation of the target; andapplying the adaptively determined coil sensitivity values to thedetermination of the unmixing matrices.
 17. The system of claim 15wherein the instructions, when executed by the processor, further resultin: adapting the regularization matrices according to differencesbetween actual ghost suppression levels for the regions and thedifferent target ghost suppression levels for the regions.
 18. Thesystem of claim 13 wherein the instructions, when executed by theprocessor, further result in: determining the regularization matrix fora first region of the different regions from the minimum element valuesof the regularization matrices of surrounding regions.
 19. The system ofclaim 13 wherein each different region comprises a single pixel positionof the image.
 20. The system of claim 18 wherein each different regioncomprises a single pixel position of the image.
 21. An MRI imagingsystem, comprising: a plurality of coils to acquire reduced k-spacesamples for a plurality of intermediate images; and an apparatuscomprising at least one processor to execute instructions to combine theintermediate images to produce a full field of view image by applying aplurality of unmixing matrices, each unmixing matrix regularizedaccording to a target level of alias suppression for a region of thefull field of view image.
 22. The system of claim 21 wherein the coilsfurther operate to acquire at least one reference image during thecourse of an imaging operation, and wherein the instructions, whenexecuted, further result in adjusting the target level of aliassuppression according to the at least one reference images.